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What is the transpose of a matrix?a.A matrix with its rows and columns swapped.b.A matrix with its diagonal elements zeroed.c.A matrix with its elements inverted.d.A matrix with its elements squared.

Question

What is the transpose of a matrix?a.A matrix with its rows and columns swapped.b.A matrix with its diagonal elements zeroed.c.A matrix with its elements inverted.d.A matrix with its elements squared.

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Solution

The transpose of a matrix is a. A matrix with its rows and columns swapped.

Here's a step-by-step explanation:

  1. Start with the original matrix. For example, a 2x3 matrix might look like this:

    1 2 3 4 5 6

  2. Swap the rows and columns. The first row becomes the first column, the second row becomes the second column, and so on. For our example, the transposed matrix would look like this:

    1 4 2 5 3 6

So, the transpose of a matrix is a new matrix whose rows are the columns of the original matrix.

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